Question

Let R be the region bounded by the graphs of y=cos((pi x)/2) and y=x^2-(26/5)x+1.

Answer 1

Let R be the region bounded by the graphs of y=cos((pi x)/2) and y=x^2-(26/5)x+1.

A. Find the area of R.
B. The vertical line x=k splits the region R into two equal parts. Write, but do not solve, an equation involving integrals that solves for k.
C. The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Find the volume of the solid.
D. The region R models the surface of a piece of glass. At all points R at a distance x from the y-axis, the thickness of the glass is given by h(x)=5-x. Find the volume of the glass.

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